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Theorem biimpac 472

Description: Inference from a logical equivalence. (Contributed by NM, 3-May-1994.)

**Hypothesis**
Ref	Expression
biimpa.1	⊢ (φ → (ψ ↔ χ))

**Assertion**
Ref	Expression
biimpac	⊢ ((ψ ∧ φ) → χ)

**Proof of Theorem biimpac**
Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 ⊢ (φ → (ψ ↔ χ))
2	1	biimpcd 215	. 2 ⊢ (ψ → (φ → χ))
3	2	imp 418	1 ⊢ ((ψ ∧ φ) → χ)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360

This theorem is referenced by: gencbvex2 2902 2reu5 3044 vfinspsslem1 4550 phi11lem1 4595 0cnelphi 4597 ideqg2 4869 nfunsn 5353 leltctr 6212 tlecg 6230 nchoicelem3 6291